If you are trying to migrate content (Sites, Lists & Libraries) in SharePoint Foundation 2010 where we don't have content deployment feature or publishing features or SharePoint 2010 and you don't have the publishing feature enabled in your site collection since you need an automated easy way to move lists or libraries from one site to another, I will be introducing a tool called "Sharegate".
Sharegate allows you to deploy/copy sites from one site to another, copy lists, folders and libraries from one site to another, Migrate Physical Share Folders to SharePoint and provides a bulk Metadata Editor.
I have a wiki library where i want to move it to another site, and i want all Wiki pages to be migrated with versions! After i downloaded this tool i got the job done in few minutes.
Screen shot with all tool features in the home page:
When you want to copy content then you have to select one of the option in the second section "Content Migration", In my case i selected "Copy SharePoint Content".